The Sahara Desert has an area of approximately 9 400 000 km^2. While estimates of its average depth vary, they center around 150 m. One cm^3 holds approximately 8 000 grains of sand. a. Approximately how many grains of sand are in the Sahara Desert? b. What fraction of the Sahara is made by 1 grain of sand? c. A small dump truck can carry approximately 20.5 m^3 of sand. Suppose a long line of dump trucks were to dump a load of sand every 30 seconds. How many years would it take to re-create the Sahara Desert?

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eudora eudora · Answer 1 · 2020-01-26T14:20:39+01:00

Answer:

a). [tex]1.128\times 10^{25}[/tex] grains

b). [tex]\frac{1}{8000}[/tex]

c). [tex]6.54305\times 10^{7}[/tex] years

Step-by-step explanation:

a). Given Sahara desert has an area of approximately = 9400000 km²

= 9400000×(10000000000) cm²

= [tex]9.4\times 10^{16}[/tex] cm²

Depth of the desert = 150 m

= 15000 cm

Volume of desert = Area × Depth

= [tex]9.4\times 10^{16}\times 15000[/tex]

= [tex]1.41\times 10^{21}[/tex] cm³

Since 1 cm³ holds sand grains = 8000

Therefore, Grains in Sahara Desert = [tex]1.41\times 10^{21}\times 8000[/tex]

= [tex]1.128\times 10^{25}[/tex]

b). Since 1 cm³ = 8000 grains

1 grain = [tex]\frac{1}{8000}[/tex] cm³

c). A truck can carry sand = 20.5 m³ Or [tex]20.5\times (10^{2})^{3} cm^{3}[/tex]

= [tex]2.05\times 10^{7}[/tex] cm³

Now time taken to recreate Sahara Desert = [tex]\frac{\text{Total amount of sand}}{\text{Sand in one truck}}\times 30[/tex] seconds

= [tex]\frac{1.41\times 10^{21}}{2.05\times 10^{7}}\times 30[/tex]

= [tex]20.6341463\times 10^{14}[/tex] seconds

= [tex]\frac{20.6341463\times 10^{14} }{365\times \times 24\times 3600}[/tex] years

= [tex]6.54305\times 10^{7}[/tex] years